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＜電子ブック＞
Asymptotics in Statistics : Some Basic Concepts / by Lucien Le Cam, Grace Lo Yang
(Springer Series in Statistics. ISSN:2197568X)

版	1st ed. 1990.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1990
本文言語	英語
大きさ	VIII, 180 p : online resource
著者標目	*Le Cam, Lucien author Lo Yang, Grace author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Statistics  FREE:Applications of Mathematics FREE:Statistical Theory and Methods
一般注記	1 Introduction -- 2 Experiments, Deficiencies, Distances -- 2.1 Comparing risk functions -- 2.2 Likelihood ratios. Blackwell’s representation -- 2.3 Historical Remarks -- 3 Contiguity — Hellinger Transforms -- 3.1 Contiguity -- 3.2 Hellinger distances, Hellinger transforms -- 3.3 Historical Remarks -- 4 Limit Laws for Likelihood Ratios Obtained from Independent Observations -- 4.1 Introduction -- 4.2 Limit laws in the binary case -- 4.3 Historical Remarks -- 5 Locally Asymptotically Normal Families -- 5.1 1 Introduction -- 5.2 Locally asymptotically quadratic families -- 5.3 A method of construction of estimates -- 5.4 Some local Bayes properties -- 5.5 Invariance and regularity -- 5.6 The LAMN and LAN conditions -- 5.7 Additional remarks on the LAN conditions -- 5.8 Wald’s tests and confidence ellipsoids -- 5.9 Possible extensions -- 5.10 Historical Remarks -- 6 Independent, Identically Distributed Observations -- 6.1 Introduction -- 6.2 The standard i.i.d. case. Differentiability in quadratic mean -- 6.3 Some examples -- 6.4 Some nonparametric considerations -- 6.5 Bounds on the risk of estimates -- 6.6 Some cases where the number of observations is random -- 6.7 Historical Remarks -- 7 On Bayes Procedures -- 7.1 Introduction -- 7.2 Bayes procedures behave nicely -- 7.3 The Bernstein-von Mises Phenomenon -- 7.4 A Bernstein-von Mises result for the i.i.d. case -- 7.5 Bayes procedures behave miserably -- 7.6 Historical Remarks -- 8 Bibliography -- Author Index In the summer of 1968 one of the present authors (LLC) had the pleasure of giving a sequence of lectures at the University of Mon­ treal. Lecture notes were collected and written out by Drs. Catherine Doleans, Jean Haezendonck and Roch Roy. They were published in French by the Presses of the University of Montreal as part of their series of Seminaires de Mathematiques Superieures. Twenty years later it was decided that a Chinese translation could be useful, but upon prodding by Professor Shanti Gupta at Purdue we concluded that the notes should be updated and rewritten in English and in Chinese. The present volume is the result of that effort. We have preserved the general outline of the lecture notes, but we have deleted obsolete material and sketched some of the results acquired during the past twenty years. This means that while the original notes concentrated on the LAN situation we have included here some results of Jeganathan and others on the LAMN case. Also included are versions of the Hajek-Le Cam asymptotic minimax and convolution theorems with some of their implications. We have not attempted to give complete coverage of the subject and have often stated theorems without indicating their proofs HTTP:URL=https://doi.org/10.1007/978-1-4684-0377-0

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